ACARA v9 CONTENT DESCRIPTION “plan and conduct statistical investigations involving samples of a population; use ethical and fair methods to make inferences about the population and report findings, acknowledging uncertainty”
The investigation cycle
A statistical investigation is a connected cycle, not a single calculation. It begins when you pose a clear question, then moves through planning and collecting data, displaying and summarising what you gathered, analysing and interpreting the pattern, and finally reporting what you found. Each stage feeds the next, so the work makes sense only as a whole rather than as a set of separate tricks. The cycle can also loop. A clear finding often raises a fresh question, and that new question sends you around the stages once more. Seeing the investigation as one connected process is the heart of this unit.
The cycle of an investigation
Five stages around a loop, then back to a new question.
a statistical investigation runs as a cycle: question, collect, display, analyse, report -- and a finding can start a new question.
Posing a clear question
Every investigation starts with a clear statistical question. A good one is about a group rather than a single person, can be measured in some way, and can be answered by collecting data. A question such as how many hours of sleep do students in our year get on a school night meets all three tests: it names a group, it asks for a number you can record, and the answer comes from data you can gather. Vague questions, and plain yes or no questions, are hard to investigate, because they do not tell you what to measure or whom to ask.
A clear statistical question
Clear, about a group, and answerable by data.
a good statistical question is clear, about a group, and answerable by collecting data.
Planning and collecting
With the question set, you plan who the population is and how to sample it fairly. Here the population is the whole year group, and a fair plan is a random sample of 40 students, chosen so that everyone has an equal chance of being picked. You then choose a suitable collection technique from the earlier units, such as a short survey, and you gather the data the same way for everyone. Asking the same question, in the same words, of every student keeps the results comparable, so that differences in the data come from the students and not from how you asked.
Plan the sample, then collect
From the whole year to a fair sample of 40.
plan the population and a fair sample, then collect the data the same way for everyone.
Displaying and summarising
Raw data is hard to read, so you organise it into a table and then a display such as a dot plot or a column graph. A display makes the pattern visible at a glance. You then summarise the distribution by its shape, its centre, and its spread. In the sleep example the dots pile up in the middle, the centre sits at about 7.5 hours, and the values spread from 5 to 10 hours. These three readings describe the whole group without listing every student, and they are what you carry into the analysis.
A dot plot of the sleep data
Centre about 7.5 hours; spread 5 to 10.
organise the data in a dot plot, then summarise its shape, its centre about 7.5 hours, and its spread from 5 to 10.
Interpreting and reporting
Interpreting means reading the summary to answer the original question. A centre of about 7.5 hours, set against a recommended figure that is higher, tells you that most students get less sleep than recommended on a school night. Reporting then puts that answer into words, in the context of the question, and states clearly what was found. A careful report also notes the limitations. A sample of 40 is small, so the result is an estimate rather than an exact truth, and a further question, such as why the figure is low, may well grow out of it.
Reporting the findings
Answer in context, with the limitations noted.
report the answer in the context of the question, and note the limitations such as a small sample.
Why this matters
The investigation cycle is how real questions become evidence, in science, in business, in health, and in government. Carrying one through from start to finish teaches you to plan ahead, to collect fairly, to summarise honestly, and to report with due caution. It also ties together every earlier idea in this strand, the collection techniques, the distributions and random sampling, and the effect of sample size, into one disciplined process. The common slip is to jump to a conclusion without a clear question, or without noting the limits of the data. This completes the Year 8 statistics units.
Quick self-check
1. What is the first stage of a statistical investigation?
2. Which is a good statistical question?
3. After collecting data, what comes next in the cycle?
4. When reporting findings, what should you include?